Question: Gabriela is 2 years older than Christopher. For the last two years, Gabriela and Christopher have been going to the same school. Six years ago, Gabriela was 3 times older than Christopher. How old is Gabriela now?
Explanation: We can use the given information to write down two equations that describe the ages of Gabriela and Christopher. Let Gabriela's current age be $g$ and Christopher's current age be $c$ The information in the first sentence can be expressed in the following equation: $g = c + 2$ Six years ago, Gabriela was $g - 6$ years old, and Christopher was $c - 6$ years old. The information in the second sentence can be expressed in the following equation: $g - 6 = 3(c - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $g$ , it might be easiest to solve our first equation for $c$ and substitute it into our second equation. Solving our first equation for $c$ , we get: $c = g - 2$ . Substituting this into our second equation, we get the equation: $g - 6 = 3($ $(g - 2)$ $ -$ $ 6)$ which combines the information about $g$ from both of our original equations. Simplifying the right side of this equation, we get: $g - 6 = 3g - 24$ Solving for $g$ , we get: $2 g = 18$ $g = 9$.